So, does installing the game help with the framerate issue or make it worse? 45 minutes in and the game is already chugging in spots. Going to install in a bit to see if it helps. I was just wondering what others experiences were with this.

I've played from beginning to end with the game installed and I got SIGNIFICANT chug in several sections of the game as well as numerous complete crashes. 
 
It probably won't help much if at all.

It's shortened load times for me.

I have mine installed and occasionally go into system settings, memory, hit the y button and then clear the system cache.  I've seen significant improvement in both frame rate and load times after playing it for a while.  I pretty much do this every time after I've played it for a few hours.  After doing this, you have to reapply any title updates (patches not DLC) you might have. 

Installing it shortened the load times for me, but it still had some framerate jumps as well some weird glitches where your gun disappears and then drops back down.  The update has improved things, but there are still a few glitches.  Haven't had any crashes since the update, though, so that's good. 

In my experience with installing games to 360, all it really does is make the 360 quieter (still got one of the old ones that is almost louder than my TV). Maybe it shortened loads for some games a little, but not enough for me to notice the difference.  
 
However, I have not tried it with New Vegas. I did it for a bit with Fallout 3 though (sadly, I only have enough room for one game, because I'm also still using a 20 GB hard drive). I would say that you should do it, because it can't hurt (much). 

I installed it last night and the load times improved significantly. The framerate was still shoddy in some spots, but nothing like I was experiencing previously. Didn't Fallout 3 also have an issue where clearing the cache occasionally on the 360 fixed some of its issues until they patched it, or am I thinking of another game?

I never had a hard crash while playing from disc, but that happened a few times after I installed to the HD. That doesn't mean it makes things worse, just saying in my experience I did not notice an improvement. It is possible that load times shortened a bit, but nothing I really noticed. Not having the sound of a chainsaw coming out of my console while I'm trying to enjoy the game is a major improvement, however.

"I have mine installed and occasionally go into system settings, memory, hit the y button and then clear the system cache.  I've seen significant improvement in both frame rate and load times after playing it for a while.  I pretty much do this every time after I've played it for a few hours.  After doing this, you have to reapply any title updates (patches not DLC) you might have.  "

Load times are definitely decreased.  I really notice it when I go in and out of buildings in towns.  There seems to be almost no delay on the loading times.  
 
No graphical improvements, though, and definitely nothing affecting the slowdown and lag.  I think these are just a result of the game's engine.  I would try the clear cache trick, because that seems to be working for a lot of people.

4.3 gigs and shorter load times. with shorter load times it should help with such things as lag in situations where the lag is caused by load times.