Most of the answers you'll get will be from professional installers (including me).
Since we usually count on making money both on the product AND the installation, many installers (understandably) get upset when they can't sell you the product, and so you're going to get a lot of emotional responses here.
I'll try to be as non-emotional as I can and explain it outright.
Whatever shop you go to, he figures on making a certain amount of money selling you his product with installation.
If you bring the product, he's likely to charge you more for the installation to try to make up for this.
In the case of an alarm or remote starter, we're most familiar with what we sell. If you bring me a brand I'm not familiar with (even if it's a good brand), it'll take me twice as long as installing what I usually sell.
The installer can (and should) always guarantee his installation, but of course won't be obligated to warranty product you bought elsewhere. (And if he doesn't sell that brand, he probably has no way to swap it out under warranty even if he wants to.)
Not all online purchases are refurbished or old-school stuff....although they sometimes are.
But it is true that whatever you buy online, your only warranty will probably be with the online seller, who may or may not be helpful and honest.
If the installer puts in your stuff and then it fails, but he and you disagree about whether the problem is the product or the install......an argument ensues. The installer ends up with either a tarnished reputation or might end up even replacing the product for free to protect his reputation................if he's smart, he'll be factoring these risks into his price.
BOTTOM LINE:
Buy it from me and have me install it, and it's all guaranteed forever. Yes, even the remotes! Whatever problem, just call me and I'll come to your house and fix it.
Buy it somewhere else but have me install it, well, I'll charge you a little more. I'll still guarantee my install forever. But if the product fails, all I can really do is unplug it from the car, hand it over to you, and tell you that I'll be glad to plug it back in as soon as you track down a replacement.
(Some installers will even charge you for removing and reinstalling the defective product.)
If it's a brand I don't deal with, and you lose a remote, I probably have no way to sell you a new one for a fair price.
WHAT I RECOMMEND:
So you know pretty much what system you want, right?
And do you like and trust this installer you've found?
Simply get two price quotes from him: One price for his system installed, and the other price for him to install the same system if you purchase it elsewhere.
Then find the online purchase price and do the corresponding math.
If you'll save a lot of money, it might be worth it to buy online and take the risk.
If it's only a small amount more, and the installer agrees to warranty everything in-house, I'd go that way.
P.S. I think anyone reputable warranties everything in-house, on the spot, no questions asked.....but not all installers agree. Some will make you wait while they ship out defective stuff for repair/replacement, even if you buy from them.......I don't think it's right to do business that way.
P.S. Also figure in the chance that you'll order/receive the wrong equipment and have to chase around about returning it. Sometimes a very small difference in a part number makes for an entirely different product.