First, I think we need to be clear that escort cards and place cards are not the same thing. Place cards go on the tables to show people which seats they are to occupy at the table. One place card is provided for each guest, with the guest’s formal social name written on it and placed centered above the place setting.
Second, we need to clarify some levels of formality. Although Black Tie is usually associated with a formal affair, there are some standards for truly formal affairs that you are probably not following. For example, at a truly formal affair married couples are never seated together. The hostess arranges the seating at every single table to ensure that each guest is seated between interesting and compatible conversationalists to whom they are NOT related, so that they can enjoy fresh conversation and enlarge their acquaintanceship. Before the diningroom is opened, while the guests are gathering in a reception room (after passing through the receiving line) each gentleman is introduced first to the lady who will sit to his left, so that he may escort her in to the table when the diningroom opens. And at a truly formal meal, filled plates are never set down before a guest (neither by a servant, nor by the guest himself who has filled it from the buffet) but rather empty plates are set down, and then filled platters and tureens are brought to the table and the guests are served from those tureens.
Now, I am guessing that although you are having formal dress, you are probably not following all these other “formal” standards — possibly not any of them. If you are, then escort cards are a MUST, especially for four hundred guests, as an escort card is addressed to the gentleman, contains the name of the lady he is to escort in so that he can find her and find someone to introduce him to her, and contains the number of the table that he is to escort her to. Since a truly formal meal requires that the hostess put great care into designing who sits next to whom, you must have place cards AS WELL. But neither of these is really expensive, except in terms of time and effort. You can make perfectly correct place and escort cards with a black pen, good handwriting, a paper-cutter, and the white cardboard from inside cheap pantyhose packages.
If, on the other hand, you are not bothering to arrange the seating at each table, and since you aren’t having a choice of plated entrees set down in front of your guests which would require place-cards with some sort of food-choice code on them, you can do without place-cards. I wouldn’t forego placecards, but I can’t imagine doing a formal dinner for four hundred without a hospitality committee to delegate the task to, either! Since you are probably not having your gentlemen guests “escort” their ladies to table in a grand procession, and probably are not arranging to have gentlemen be introduced to a strange lady as their dinner partner, you also don’t need escort cards to facilitate that function. So, the only purpose for escort cards would be to tell families which table to sit at. They work fine for that purpose — but so does a seating chart. So choose one or the other, but you don’t need both.