Two things. One, this all depends entirely on the weather. Two, it's entirely of benefit to climb as high as you possibly can, and it doesn't matter if it's a jet or a piston engine. It's just that jets have a lot more trust and can maintain higher speeds, so it's not as much of a struggle as a prop plane is to climb.
All planes are effected by the same physics, when you give, you get, and it all happens in mostly equal quantities.
At low alt you have dense air which creates lots of power and the engines don't have to work hard, but that air functions as wind resistance. At high alt this reverses and although you have the benefit of thin air air also holds back your engines. Really it's a question of engine power. Since the B377 has so much of it, you can really fire up the engines if you want to.
At high alt you also have less gravity, which helps. It's not much, but it helps. I think at 40k it's a 0.4% reduction.
When it comes down to it, higher is better because of thinner air. It's more efficient. To prove my point, what's a B377's fuel economy in outer space? Infinity.
I mean, I'm just proving a point, here. Higher is most certainly better, as long as, you know, you can get there.
But the question is, SHOULD you try? That depends. It takes a lot of engine power and fuel to climb and doing so is inefficient compared to just cruising, so the benefits of the high cruise need to outweigh the climb. The price you pay for climbing is very substantial. In my extreme example, the fuel it takes to put a spacecraft into orbit does not outweigh it's otherwise infinite fuel economy if your goal was just to get to the other side of the planet. You use 5% or 10% of your total fuel capacity in your B377's climb at max gross weight. That high alt had better be worth it. Is it?
Check out the winds aloft. You absolutely need to do this. Look at the different flight levels and see if the winds change much. You have to be weary of high altitude winds because they can be pretty epic. 100+ knots! But then again, they can be pretty epic in your favor.
So you can break down your cruise altitude into three conclusions.
Winds aloft are horrible: Climb just high enough to get out of the clouds/weather/turbulence/terrain and just cruise there.
Winds aloft are awesome: Float that joker as high as it'll go and ride the waves. Very low IAS okay since you'll have epic winds pushing you.
Winds aloft/flight plan are substantially variable in direction. You may have to do some step climbs or descents. Generally speaking step climbs okay and step descents you should be weary of, since you burned a lot of fuel to climb. As long as your flight profile has all of the ups before all of the downs, you should be good and feel free to get complicated to avoid those winds.
How high is the limit to climb a B377? The plane has way too much power and is limited by it's pressurization limits, but the established service ceiling of 32k or 33k is a pretty good upper limit. For a traditional, realistic flight you don't want to exceeded that.
I'm usually pretty lazy in my climbs, no more than 500 f/m, and descents are also lazy. If you're getting less than 300 f/m at climb power you should seriously consider if you should stop climbing. I use the 300-rule on all my flights in all sim aircraft as a decision point about the ceiling of my flight.
Hope that helps.