OK - we know that the engine makers HP numbers are not real world. But I would guess that a motor claiming 2 HP and a motor claiming 1 HP, by the same manufacturer, the numbers would be relative. That is, the 2 HP would have twice the power of the 1 HP motor. An OS .46 AX claims 1.7 HP at 16,000 rpm. An OS .65 LA claims 1.7 HP at 16,000 rpm. The .46 also weighs 6 oz. less.
The Hobbistar comes with .65 LA - weight 7-8 lbs.
That being said let, me get to the question. If I put a .46 AX on a Hobbistar with a smaller gas tank and the motor being lighter, would it have the same or similar performance as with the .65 LA? ( yes it would need to be rebalanced )
On a side note the tower trainer 60 says use a .46 to .61 engine - weight 7.5 lbs.

If these figures were genuine then both engines would need to be fitted with the same size prop (roughly, an APC 10x6 would be close) to get those revs. With that prop then the model would fly much the same with either engine. But load the engine down with bigger props for real world flying (say, somewhere around 11-12,000 revs) and you'd find the smaller engine would be bogging down way below the larger one. The 65 would easily handle a 12x6 or larger but not the 46. The extra low down grunt more than outweighs the extra weight of the larger engine. That extra 6 ounces on a 7.5 pound model is only another 5% extra all up weight.

Yup, the smaller engine is rated at the same horsepower as the larger. And on your Hobbistar, the 46 will probably haul the sucker about the same as the larger engine can. There are two details however...........

The difference of 6 less ounces of engine weight will have an effect on how the model balances. So if all you do is swap the engines and tank, the CG of the plane is going to move aft. You need to check the CG now. If it's already toward the rear of it's suggested range then you need to be prepared to move the battery forward. If there is no room to do that, then you are going to need to either move servos or add weight. If you have to add weight, ask yourself why you're doing this. You shouldn't just let the CG change and see what happens next time the model flies. You need to deal with it before, not after.

Also, the two different engines swing different diameter props. The larger engine's larger prop can give more thrust. Not always, but usually. The prop diameter is the major player in how well the engine pulls the model. But put identical horsepower to different props and you don't always see different thrust. But it's not possible to predict. So be prepared for possibly a bit less thrust. You'll see it, if it happens, on takeoff first. The model may take longer to get airborne. It may not climb as well. But don't make your judgement on one takeoff and climb. Make sure you have a good needle setting and then try a couple of different props. And don't expect to get full power out of a brand new motor.

downunder,
Actually, it sounds reasonable that two different engines that advertise the same rpm range and HP ratings should spin the same prop at the same rpm, but it often doesn't work out that way. With little 2strokes, their timing, compression, and spinning mass often produce different torque curves that do peak about the same value but with different loads. The engines won't spin the same props the same rpm. A 65 would be designed to put it's peak power into the 12-13" props and do it at moderate rpm. A 46 would be designed to spin 11" props at higher rpm.

If I had to bet, I'd bet that the 65 would be spinning faster than it's design peak with a 10-6. But the 46 wouldn't be as far off it's design peak. And after messing with a bunch of 46AXs, I'd guess the 10-6 would be a bit small for it's envelope as well. Mine seem best with 11-6s. For those two to be compared with one prop, the prop ought to be within each engines envelope, and as far into each envelope as possible.

When you run most 2strokes outside their design envelope, they often don't produce power worth spit.