I think, as Jan Niemcyzk's rather excellent "The Last War" on TBOVERSE shows, defence spending throughout the West would remain markedly higher, especially in countries that made more dramatic cuts, which come the recession and financial crisis that most of the world is currently in, means one of maybe two or three things (assuming butterflies don't change things):
1)Greater public expenditure means national debt even higher than it is now, especially in the US and UK (I would guess this would be the most likely outcome, although how much defence spending in the UK would increase is questionable)
2)Spending in areas such as the NHS doesn't reach the stratospheric levels seen in the last decade or so, as resources are arguably more urgently needed for defence(Unlikely, although butterflies may prevent everyone's favourite chancellor holding power)
3)The greater industrial base in countries such as the UK supported by increased defence spending would lead to less reliance on the financial sector, thus making the situation not as bad as it is now (What I would personally like to happen)
Looking at it from the perspective of the UK's armed forces, primarily the Royal Navy, I think several things might change;
-there would be at least the 12 T45s originally promised (maybe more, TLW shows a Navy with 14),
- the new carrier/s design would likely be different- I think that if the Navy's primary role continued to be ASW in "the big one", then Invincible-esque "through-deck crusiers" would be more likely than bigger strike carriers (Although we could get both

),
-at least 8 Astutes would be ordered
-the frankly moronic decision to cancel the Nimrod MRA4 would not go ahead
-the design of HMS Ocean might be different-I've always understood it to be that the use of commercial features is one of the reasons the ship is so "tired", there might be 2
-less Type 23s and 42s would be retired
-The Upholder class would not be sold without replacement
-Older platforms, such as the Harrier, Sea King etc might be replaced sooner
In conclusion, I think the Navy would be much healthier in this scenario. It would still have a well-defined role the public could "get", and there wouldn't be as much inter-service squabbling, which the RN always seems to come out of badly. I'm afraid I can't share Jan's optimism regarding procurement though( 6 Astutes, 10 T45s and 10 T46s ready on schedule without massive delays?!?)