This entirely depends on what your purpose of playing is. At issue here are two independent factors, expected value and variance. I’m going to take a little detour to explain, and then return to your question.
Expected value is the probability of winning multiplied by the win amount, minus the probability of losing multiplied by the amount lost, all divided by the amount wagered. For roulette, every bet on the board except for one (the 5-square bet) has the exact same EV. Note that EV doesn’t depend on how much you wager - it’s expressed as a percentage loss (if negative) or gain (positive).
$10 on a 1-square bet: ((1/38)*350 - (37/38)*10)/10 = -0.053
$5 on 2 1-square bets: ((2/38)*170 - (36/38)*10)/10 = -0.053
Neither system will make you more or less money in the long run.
However, the other thing to consider is variance. Variance is a measure of how often your actual result is close to your average result. Things with high variance often deviate from your EV, things with low variance will frequently be close to your EV.
In your example, putting $10 on a 1-square bet has a much higher variance than putting 2 $5 bets down. In the first case, 1/38th of the time you will be up (but way up), 37/38ths of the time you will be down. In the second case, you’ll be twice as likely to be up, but you’ll be less rich if you hit. To go further, let’s say you put 10 $1 1-square bets down. Your EV is still the same! ((10/38)*26-(28/38)*10)/10 = -0.053 But now, you’ve got a 26% chance of being in the black the next round.
Getting back to your original question, let’s figure out what your goal in playing is.
(a) You want to turn $10 into $360 with no regard to how long you play. Your best bet now is to plunk down all $10 on one number and pray. Remember - every bet in roulette has a negative EV, so you basically want to ride the variance. You’ll meet your goal about 2.6% of the time.
(b) You want to turn $10 into $70 with no regard to how long you play. Your best bet now is to spread out and make 5 $2 bets so that if any one of them hits, you’ll make your $70. You’ll meet your goal about 13% of the time.
(c) You want to play as long as possible on $10. This is the goal of most gambling. In this case, you now want to lower your variance as much as possible. As a matter of fact, you shouldn’t be betting on single numbers at all - you want to bet as little as possible so you get the most bets in, and cover as many numbers as you can with each bet. For example, if the table is a $5 minimum, you want to make $5 bets on one of the following: red, black, 1st half, 2nd half. You have a 70% chance of making it past 2 rounds.
(d) You want to have the highest EV possible. Take your money and deposit it in an FDIC-insured bank. 99.99999% guaranteed.