Given its ambition, money was tight on the original series, but it wasn't a "cheapie" by any means. The first season's average budget of $190,635 was comparable to other one-hour dramas of the time. However, it didn't help that the series' budget was slashed each season while simultaneously incurring annual contractual pay raises.
Having said that, the average first season budget would have yielded about $670,000 in 1987. Since TNG had a budget of $1.3 million per episode when it premiered (which later went up, unlike the original), there was certainly more money to go around on the sequel series.