A seed packet and a punnet of seedlings both get you to the same end point, a mature vegetable plant, but the cost, time and choice involved are genuinely different. Neither is the automatically "better" option; which one makes sense depends on the crop and what you're trying to get out of your garden.
Cost is the most obvious difference. A single seed packet typically holds anywhere from a dozen to several hundred seeds and costs a few dollars, while a punnet of seedlings from a garden centre usually holds four to six plants for a similar or higher price. Sown and grown on successfully, one packet of seed can produce many times the number of plants a punnet does for roughly the same outlay, which matters most if you're planting a lot of the same vegetable, want to succession-sow over several months, or are trying to keep the overall cost of a vegetable garden down.
Sown and grown on successfully, one packet of seed can produce many times the number of plants a punnet does for roughly the same outlay
Time works the other way. A seedling from a garden centre is already several weeks old, past the vulnerable seed and early-seedling stage, and closer to fruiting or harvest than something you sow yourself. If you're planting late in a region's window, want a quick win, or are replacing something that's failed partway through the season, buying an established plant gets food on the table faster than starting from seed would.
Some crops are genuinely easier to raise from seed at home than others. Direct-sow vegetables that resent having their roots disturbed do best sown straight into the ground rather than transplanted: carrots need loose, stone-free soil worked in place to grow straight, unforked roots, and dwarf beans, climbing beans and peas are all reliably easy, quick-germinating crops that are simply sown direct where they're going to grow, no trays or transplanting required. Buying seedling carrots, beans or peas isn't really an option at garden centres for this reason, and growing your own from seed is usually the only realistic route for these crops anyway.
Other crops are more often worth buying as seedlings, at least while you're building confidence. Tomatoes and capsicums both need consistently warm soil to germinate reliably and are commonly started indoors or under cover well ahead of their outdoor planting window, which is more setup than a beginner necessarily wants to take on. Celery is slower and patchier again: it's rated a genuinely difficult, advanced crop to grow, with a long season and seed that germinates slowly even in the best conditions. Buying these three as seedlings skips the fiddliest part of the process and gets you straight to the part of growing them that's actually rewarding.
Variety is where seed has a real edge that buying seedlings can't match. A garden centre's seedling range is limited to whatever varieties sell well enough in bulk to be worth propagating and trucking out to stores, generally a handful of reliable, well-known types per vegetable. Seed catalogues, by contrast, list dozens of varieties of the same crop, differing in flavour, colour, disease resistance, days to harvest and growing habit. If you want anything beyond the standard supermarket-style tomato or lettuce, seed is usually the only way to get it.
In practice, most home gardeners end up doing both: seed for the crops that are cheap, easy and direct-sown anyway, and seedlings for the crops that are slow, fiddly or disease-prone to raise from scratch, especially while you're still finding your feet.