Bet on 1X2 only when we are really sure that the underdog team will win, why not place bet with handicap to minimize the risk?
Always betting on favorites or underdogs is also not wise, so it cannot be said which one is better.
If we could win consistently by betting on favorites or underdogs again and again, all sportsbooks would be closed their service since a long time ago.
If you take a deeper look into it, think that you would get the same result by betting following your analysis or your guts as by always betting on favourites or underdogs. It is all about the odds, and the odds are extremely well calculated by sportsbooks. It may sound counterintuitive, but the same principle is applicable to lotteries for example, where you have the same chances of winning picking up the 1, 2, 3, 4 and 5 instead of the 2, 17, 32, 43 and 45.
It has been said before: betting is about adrenaline (and/or dopamine?), and if you enjoy always betting on favourites or underdogs, I don't think it is worse than any other strategy.