I think it depends on the intended use.
You mentioned "one knife that can do most things". Opinions will vary greatly about how a 7" - 8" bladed knife will be primarily used and what is preferred for Most things or even what Most things means.
Personally, I feel that most knives with blades around 7 start reaching the balance of versatility vs. some chopping ability.
8 blades (generally) start leaning towards mid-sized choppers and often start losing some of their versatility. (*** The NMSFNO might be one of the best examples of a good balance of maintaining versatility while still reaching very worthy chopping ability!)
I think UJ's simple answer is pretty good in regards to "CHOPPING", the extra weight of .25" over .1875" is significant. There is easily a noticeable difference between .25" and .1875"
I think it worth pointing out that blade thickness is not the only factor in chopping ability, blade weight and so on. Aside from length, there are at least three other very significant considerations/factors: blade shape, blade height and blade grind.
In regards to blade shape, consider a bolo styled blade puts a lot of extra weight forward that aids in chopping.
Blade height should similarly be self explanatory. A 2.0" tall blade at 0.1875" would have about the same blade mass/weight as a 1.5" tall 0.25" blade. Other variations in height vs. thickness would give various results.
From what I have noticed (and "feel" is subjective), taller blades (especially at towards the tip) seem to feel better for chopping (to me). But, a taller skinnier blade won't be so great for prying.
Consider that most machetes are very thin and most often under 0.1" thick. My Tramontina is only about 0.083" thick. (* A .25 blade is pretty much exactly 3 times the thicker!!!). Yet, a thin machete can still chop many materials VERY well. But, I would say a machete doesn't baton well and doesn't have sufficient mass for chopping large wood. Still, a good machete, can have lots of power and ability for chopping limbs up to 2" - 3" thick. (Jason probably made a good de-animation choice especially considering bang-for-the-buck!) Considering how thin and light a machete is, if a good edge is put on a worthy machete, a machete is still an amazing tool (and/or weapon)! - I have to say the $10 - $20 price tags are very worthy of mentioning as well. But, most machetes are hardened in the low 50's or less. So, they don't hold edges anywhere near as long as any knives including INFI. So, there are still obvious advantages for well made heavy duty knives. But, the gained advantages (and some compromises as machetes are light, with speed and reach) of heavy use knives vs. cheap machetes come at exponential price increases..... sorry for the tangent.
Full flat grind, Full Convex grind and Sabre grind all affect the weight of a knife. A sabre grind .1875" knife still won't weigh as much as a .25" full height flat grind of the same height, but the difference is less than if grinds were the same.
For chopping, I like more blade forward weight. But, for all-around use, I like more balance.
For carry, I prefer "Lighter" and tend to always prefer all-around abilities over straight chopping ability. But, that is me.... and even that is subject to personal preference on a given day.
Considering how tough INFI is, I think most any knife made with .1875" stock would/should still be PLENTY tough enough (at least for me! - I honestly don't pry with my knives). I am confident, if prying or putting similar heavy lateral torque onto an 8" blade, you would notice a lot more flex and bend in a .1875" x 8" INFI blade vs. a .25" x 8" INFI blade. However, I am also confident that a .1875" x 8" INFI blade would still handle/take a LOT of abuse.
For comparison, short of very limited rare variations, the longest blade I can think of with a 0.1875" blade is the SarSquatch with a 7.0" blade. The Hell Razor follows that with a 6.625" blade, followed by the Skinny Ash with a 6.4" blade. Most anything else even close to 7" let alone 8" is at least .22" and mostly .25" and up.
For my preferences in a 7" - 8" blade, even my choices are getting muddier all the time. The Sarsquatch has become one of my Big-time all around mid-large all-around knives. It has much less chopping ability compared to a FSH, NMSFNO, Chop/Ratweiler, or similar thicker knives. But, the balance, feel, weight, and carry-ability, etc. are awesome for so many other tasks.
Sorry to mention here, but the Camp Tramp with a 7.325" x .236" thick blade at 14.5 ounces total is still an awesome all-around light-weight mid-large knife. The Scrap Yard SOD should also be very good. But, I am sure I will prefer my Camp Tramp without the ramp, with a better choil (IMO) and I prefer SR-101 with better edge properties even if SR-77 is tougher.
The Sarsquatch weighs about 17.0 ounces even with its thinner 0.1875" thick blade. The Camp Tramp has a more forward weight balance with Res-C handle and smaller tang. The Sarsquatch has more even balance with full tang and micarta scales.
For the most chopping ability at 8" or less, the HH (HHFSH) is probably the king. I used to have one and one of my biggest regrets for selling. But, while it's awesome mass was/is great for chopping ... and just holding/drooling over in pure awe, I feel its mass really was a bit of a detriment in real-world all-around use and carry. I have a regular 0.25" thick FSH coming from the last Ganzaaa to help relieve my loss anxiety of my HH. I assume the regular FSH is still a slightly better chopper than the NMSFNO. The regular FSH has a sabre grind so probably a little more blade weight and forward weight than the NMSFNO. Also, the Fusion handle on the FSH is just a little better for chopping than the SF handle IMO. But, I think the SF handle is a little more versatile for all-around use than the Fusion handle.
**** HOWEVER, the new NMSFNO is an AWESOME and INCREDIBLE knife. For those of you on the fence about purchasing one, I say GET IT.
IMO, the NMSFNO, might not be as good at chopping as the FSH and especially the HH, but IMO, the NMSFNO has more large-knife all-around capabilities while still being a good chopper compared to most any knife I can think of.
IMO, 9" - 10" knives like the FBM, Battle Rat, Dog Fathers and such are all really PURE choppers and great for batoning to me and don't really provide much versatility. Sure, the big knives can be used for lots of things if needed. But, not ideal IMO.
The differences in 0.1875" vs. 0.25" thickness is back to personal preferences for feel and intended use and the weight distribution (blade shape. height, grind) vs. balance.
Sorry if my answer is a whole lot of nothing. But, basically I don't think there is a simple single answer.
Hope that helps.
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So the difference is actually very large. 
:thumbup: