I like both meat and vegetarian but favour vegetarian curries. I realise that Indian religious traditions have links to vegetarianism. Although globally, curries often have cream and the meats in meat curries aren't all that lean, yet (despite meat curries being so sinfully tasty) an alternative is vegetable/legume curries that have fewer calories, fibre, as well as good nutritional value. They don't feel as heavy and won't cause severe heartburn - the fibre in the vegetables/legumes counters the heartburn-causing spices - even more profound when consuming with coffee or alcohol. So vegetarian curries are both consumed for religious and less religious purposes. I think vegetarian curries are the healthy choice on Indian menus, and fortunately, vegetarian options are quite heavily featured on Indian restaurant menus, with cauliflower, eggplant, dried fruits, spinach, chickpeas, all colours of lentils, potato, pumpkin and kidney beans all healthier choices.
It should be noted, curries are served in other cuisines, such as Thai, Japanese, Malay as well as Indonesian, Pakistani and Sri Lankan and several others. Interestingly though, the question applied to all cuisines, so just to clarify, I focused on Indian Cuisine because curry is so synonymous with it - in terms of the number of consumers Indian makes an ideal focus for a longer discussion. However, the other cuisines make the question quite a broad question, for example, I like daal the best in Indian but massaman beef in Thai as a favourite, in fact, I prefer meat-based Thai curries as a close preference over tofu and vegetable-based so it's definitely wise to mention those differences. Also true that vegetarian options are likely cheaper as well, so for any frugal people around the world vegetarian is a good idea. If I had to make a quick global or universal answer, I'd say vegetarian - for frugal, health and interest reasons.
Of course, out of respect for religions, I don't think giving specific examples is a constructive thing to do, at least to me, but on the linked pages for vegetarianism, some Indian religions are clearly linked to non-violence towards animals. It can feel exciting to think of such places where things are done with such a difference in mentality, and I find India (the nation) and vegetarian cooking are harmonious. However, meat curries, tandoori cooking and meat biryanis are such enduring and delicious mainstays of this popular cuisine, and so I totally appreciate any answer in terms of loving a good butter chicken, a tandoori chicken or a goat or fish biryani.
In terms of an alternative yet healthy approach, I have added a yoghurt chicken recipe based on a search for 'spiceless' Indian cooking for fans of meat-based foods. For vegetarians, I found soaking lentils overnight and washing/draining them, adding a veggie stock and a hint of garlic and salt yet making them as a stew or 'spiceless daal' was my response to spices in my daals causing heartburn. It's fine to have with a mocha cola or a regular cola instead as a fun and energetic meal - as lentils improve brainpower - a rather wicked anytime brain/studying boost.
In terms of Indian cuisine, however, an example of my tendency towards vegetarian options at Indian Restaurants is here, where Deepak on a weekday afternoon made a memorable Daal Makhni, hence it's linked to show I indeed favour the vegetarian curries. I think that afternoon shows hints about the Indian religions, how their people have distinctive qualities and thus there are many sides or aspects to Indian nationality - how can there not be with such a huge population and ancient history? It's truly a fascinating question because it's capable of bringing about extensive discussion or a simple answer as to are vegetarian curries better than meat curries?