Rotterdam City Card
I personally do not think that the Rotterdam City Card will be of much interest unless you love visiting museums or the Rotterdam Zoo. Even then, the card gives you ticketing discounts rather than free entry, which further makes it less appealing.
Similar to the I Amsterdam City Card, the Rotterdam City Card also covers unlimited public transport costs.
Museum Pass (Museumkaart)
Before I go into the details of the Museumkaart, it is important to highlight that there is one meant for residents of the Netherlands, as well as the temporary Museumkaart meant for visitors.
The temporary Museumkaart allows a visitor to visit any 5 museums in the Netherlands within 31 days, all for a cost of €75. Particularly, it also includes the Anne Frank House and Van Gogh Museum, both of which are not covered by the I Amsterdam City Card.
The temporary Museumkaart can only be purchased at participating museums, so you need to do so at your first museum visit. For this reason, I wouldn’t really recommend using the temporary Museumkaart for Anne Frank House. This is because the Anne Frank House tickets are sold out very quickly and you are not likely to be able to find a ticket if you haven’t booked one before your arrival.
Further to that, it is also unclear which museums are covered by the temporary Museumkaart. Information is scarce online and so I wouldn’t recommend risking the purchase of this card.
Museumkaart or I Amsterdam City Card
The Museumkaart is great if you intend to visit 5 museums, especially those with high entrance fees. For example, each entry to Rijksmuseum costs €25 and Nieuwe Kerk €20. So 5 of such visits definitely makes the Museumkaart worth it. As mentioned earlier though, information on what the temporary Museumkaart covers is quite scarce online. Therefore getting this card may carry a slight risk without knowing exactly what is not covered.
On the other hand, the I Amsterdam City Card also includes walking tours, public transport and other activities, not limited solely to museum visits.
Therefore you should pick the activities you are interested in and then work out which option works the budget better. Personally, I would recommend the I Amsterdam City Card based on the clarity of what the card covers.