For most jobs, I build Bobcats as they are faster and can fill most defensive roles that a Grizzly usually fills, but with a 2 scrap discount. They aren't the best unit to be piloting though and when they are facing an opposing force of Grizzlies escorting a Human player, the Human with the AI Grizzlies will usually win.
I relegate Bobcats as escort units to mainly Scavs, "Hunting" Thunderbolts, and Sasquatches. I've had Sk-8080 try to advance on my base on Theater O'Pain, but had to get through my scavs which were followed by Bobcats. The Bobcats distracted Sk long enough to allow the Scavs to retreat and long enough for me and two hunting Thunderbolts and two more Bobcats to finish off his forces. He lost about 5 or so Czars and 3 or so Flankers, plus himself in a Twin-SP Czar.
On another note... I don't usually upgrade units in a strat, as I believe than the downside of losing them too easily far outweighs the benefits. However, SPs, in my opinion, tend to augment them for base assaults and are very cost effective to the Grizzly (8 + 5 + 5 = 18 ; 6 + 5 = 11), but I favor stock as the spray from the ATs tend to be far better against people with high FPS and people who have "Lag armor."
I also believe that the Bobcat is a better replacement for the Razor, as both units cost 6 scrap and the Bobcat fares better in a fight than a Razor, but don't get me wrong, the Razor has it's roles too.
In DM, I use one of two combos for the Bobcat, SP-Shadower and/or "MAG 'n' TAG." SP-Shadower tends to be a little bit undodgable while the latter tends to be a one-two punch. Bobcats in DM tend to be vulnerable to Czars, Stealth Grizzlies, Black Dog Grizzlies, and some Ace Bomber opponents, while they tend to be more durable against Scouts and normal Bomber opponents. Turrets and Walkers are helpless against Bobcats using hornets, and Rocket Tanks have a hard time locking Hornets on them. (especially if the person is piloting a Black Dog Bobcat, then they can use Phantom VIR and prevent lock-ons on both Shadowers and Hornets; Spork showed me that when I was piloting a Wolverine

)
This was just observations, as the true test of the mettle of the Bobcat starts with you.
EDIT: Changed last sentence to be relevant to the whole post.