Used diesel buying question

I'm pulling a travel trailer now that, ready to go, is about 6500-ish. The Suburban can do it, in the short run. But, it's really working hard. I'd keep my trailer for sure as we think it's perfect for what we do. I have been pulling travel trailers on and off for a number of years and always with gassers. None of them have ever been really great at it. I keep hearing about how great diesels are for towing. My guess is that for 6500 LBS of trailer it would be pretty awesome. At the same time, I use my Suburban as a daily driver and I'd need a truck to get me back and forth 95% of the time. I like the 4x4 option as I occasionally need it. The Suburban has been reliable so far. The 5.3 is decent on gas but, really pretty close to maxed out at times when towing the trailer. I have read that the 6.0 GM V8 is a modest improvement. I don't want to commute with an 8.1 2500 Suburban gasser. The diesel seems like a good option.