Cross-country skiing and snowshoeing originated as a means of travel in snowy terrain in the winter. The sports have both evolved over the years. Modern snowshoes are lightweight and easy to use and work with almost any type of boot; some, like racing, or speed shoes, can even be used with running shoes. Cross-country skis have gotten lighter, and the bindings have improved as well, making them easier to turn. Both types of gear have their advantages.
If you can walk, you can snowshoe. Snowshoeing is little different than walking, especially in the speed snowshoes, which have a trimmer, shorter profile, enhancing the ability of the user to run in the shoes. Cross-country skiing is easy to pick up on level terrain, but as the terrain gets hillier, different techniques are needed, especially for making turns and controlling speed when moving downhill.
If your primary goal is to explore mountain terrain or forests in the winter, snowshoes have better maneuverability. Especially when traveling uphill, snowshoes, with their built in crampons providing traction, are easier to use. Cross-country skis have better flotation in deep snow since they have more surface area. However, when using then to travel uphill, you need to either use grip waxes or special waxless skis with a fishscale pattern that provides grip. Alternately, serious backcountry skiers use stick on climbing skins on the skis, which cover the entire base and prevent the ski from sliding backwards, while enabling a normal step glide motion.
Snowshoes are cheaper than cross-country skis, mainly because the binding is integrated into the snowshoe and the user can put snowshoes on almost any boot they have. Snowshoes generally sell for between $150 and $250. Cross-country skis sell for $120 to $300. The bindings sell for an additional $60 to $100. Cross country-boots that fit the bindings sell for between $120 and $300.